19 - Modelling of disorder

Summary

Introduction

In this chapter we shall model the thermodynamic effect of some physical phenomena. In each case we shall start by defining an internal variable representing the extent of the physical phenomenon to be discussed. We shall proceed by deriving an expression for one of the characteristic state functions in terms of the internal variable together with a set of external variables. The choice of characteristic state function depends upon what set of external variables is most convenient. Then we shall calculate the equilibrium value of the internal variable by putting the driving force for its change equal to zero. Finally, we shall try to eliminate the internal variable by inserting the expression for its equilibrium value in the characteristic state function.

Our derivation of an expression for the characteristic state function will usually be based upon two separate evaluations, one concerned with the entropy due to the disorder created by the physical phenomenon and the other concerned with what may be called the non-configurational contribution. The entropy will be evaluated from Boltzmann's relation which is here preferred because it is felt that it gives a better physical insight than the more general and elegant method of statistical thermodynamics based upon the use of partition functions. The purpose of statistical thermodynamics is to model the thermodynamic properties of various types of systems from statistical considerations on the atomic level. The relation proposed by Boltzmann can be derived from such considerations.